You were given f(x) = x/2∏ for 0<x<2∏. Your function is not defined at x = 0 or at x = 2∏. So you don't have f(0) = 0 and f(2∏) = 1. The value of a function like that at the two end points is irrelevant in calculating things like the Fourier Series so they are usually left undefined. If you insist on defining f(0)= 0, then you have no choice but to also choose f(2∏) = 0 if you want the function to be periodic.